ANSWER TO QUESTION 1
The equation of a line in slope intercept form is given by the formula,
[tex]y = mx + c[/tex]
where
[tex]m[/tex]
is the slope of the straight line and
[tex]c[/tex]
is the y-value of the y-intercept.
It was given in the question that, the slope is -4.
Thus,
[tex]m = - 4[/tex]
It was also given that the y-intercept is -3.
Thus,
[tex]c = - 3[/tex]
Therefore the equation is
[tex]y = - 4x + - 3[/tex]
This gives us,
[tex]y = - 4x - 3[/tex]
The correct answer is A
ANSWER TO QUESTION 2
We were given that the equation passes through the two points (-2,1) and (2,1).
We can see from the points that the y-values are constant. This means that the line is parallel to the x-axis
Therefore the equation is given by
[tex]y=y_1[/tex]
where
[tex]y_1[/tex]
is the constant y-value.
Thus, the equation is,
[tex]y = 1[/tex]
or we write in general form to get,
[tex]y - 1 = 0[/tex]
The correct answer is A.
We could have also decided to find the slope,
[tex]m = \frac{ 1 - 1}{2 - - 2} = \frac{0}{4} = 0[/tex]
using any point, say
[tex](2,1)[/tex]
we plug into the point slope form formula to get,
[tex]y - 1 = 0(x - - 2)[/tex]
This gives us
[tex]y - 1 = 0[/tex]
ANSWER TO QUESTION 3
The equation of a straight line in the slope intercept form is
[tex]y = mx + c[/tex]
where m is the slope and c is the y-intercept.
Thus,
[tex]m = - \frac{1}{3} [/tex]
and
[tex]c = \frac{10}{3} [/tex]
We substitute in to the formula to obtain,
[tex]y = - \frac{1}{3} x + \frac{10}{3} [/tex]
we multiply through by 3 to obtain,
[tex]3y = - x + 10[/tex]
We rewrite in general form by equating everything to zero.
Thus,
[tex]3y + x - 10 = 0[/tex]
Or
[tex]x + 3y - 10 = 0[/tex]
The correct answer is option D.
ANSWER TO QUESTION 4
We want to write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).
This implies that the line passes through the points,
[tex](-3,0) \: and \: (-3,7)[/tex]
We find the slope as follows,
[tex]m = \frac{7 - 0}{ - 3 - - 3} = \frac{7 - 0}{ - 3 + 3} [/tex]
This implies that,
[tex] m= \frac{7}{0} [/tex]
The slope is undefined. This means the line is parallel to the y-axis.
The equation of a line that has an undefined slope or parallel to the y-axis is given by
[tex]x=x_1[/tex]
where
[tex]x_1 = - 3[/tex]
Therefore the equation is
[tex]x = - 3[/tex]
The correct answer is A.
or you could have also obtained the equation as follows using any of the points.
[tex]y - 7 = \frac{7}{0} (x + 3)[/tex]
This implies that,
[tex]0(y - 7) = 7(x + 3)[/tex]
[tex]0 = 7(x + 3)[/tex]
We divide through by 7 to get,
[tex]0 = x + 3[/tex]
hence
[tex]x = - 3[/tex]
